LSU linebacker Jacob Phillips is being investigated for rape -- after a female LSU student athlete filed a report with police ... TMZ Sports has learned.

Phillips has not been arrested or charged with a crime -- but we've confirmed the Baton Rouge PD is actively working on the case. We're told he strongly denies any wrongdoing.

Here's what we know ... cops were called to a Baton Rouge hospital on June 11 to respond to a woman who claims she was sexually assaulted by Phillips early that morning.

18-year-old Phillips was a prized recruit for LSU -- he was ranked as one of the top high school linebackers in the country.

Sources with direct knowledge of the case tell us ... the accuser claims she had a previous romantic relationship with Phillips but had cut things off before the alleged incident.